Water supply and the environment

Once upon a time, the citizens of a large city realised that their water supply was running low, and as the city was expanding, and the demand for water per capita was increasing, there was a problem of supply. So they looked to the mountains to the north and to the west, where there was high rainfall, and few people lived there (though there were many sheep) and asked some engineers to investigate where it might be possible to build a new reservoir.

And after some time, and after spending some of the city's money, they returned and announced that they had found an ideal site, which would mean displacing many sheep, but very few people. "What is more," they said, "although the site is about one hundred miles away, there is a convenient river which flows from the site towards the city, and could be used to convey the water part of the way from the reservoir to here. If you pay us some more money, we can devise a scheme to extract the water which will be released from the reservoir." And the citizens thought that this was a good idea, and the engineers devised a suitable scheme. Everyone was pleased because this solution was very good for the environment, as it did not need pipes to be laid through the beautiful mountains.

In due course, the people who lived by the river heard about the scheme, and went to the citizens of that city, and said: "We know that your reservoir is going to supply you with water. We would like you to help relieve us from the problem of floods. Please will you plan your reservoir so that it can hold back the water at times of floods?" They too were concerned for the environment, because they farmed and fished beside this pleasant river.

So the citizens listened, and as they wanted the people by the river to support their expensive water supply scheme, they agreed. But when the engineers who had devised the scheme heard of this, they were shocked, and said, "That means conflicting objectives!" For the benefit of the citizens, they explained. "If you want to supply water, the reservoir must be full. If you want the reservoir to hold back flood water, it must NOT be full. Water supply and flood protection are conflicting objectives."

"What shall we do?" wailed the citizens. "We need water. The people by river do not need floods." And one of the engineers announced, "The experts in conflicting objectives are called Operational Research Scientists. You must go and consult with some of them." So the citizens went with a bag of money to consult with a team of O.R. Scientists, who said that this was the sort of problem which they could help with, and appointed some of their number to work with the engineers.

The O.R. people, as is their habit, started asking questions about "the system", and as is their habit, started to read about other places in the world that such a conflict of objectives had been found. And they discovered that such a problem had been given a name, the "Noah-Joseph problem". Noah, in the Bible, had been involved with a flood. Joseph, also in the Bible, had been involved with a seven-year drought in Egypt. Floods occur very rapidly; droughts occur very slowly. They also discovered that there were some further environmental constraints and conflicts. First, the water from the reservoir would flow into a natural lake, and there was a town beside the lake which was liable to flood if the lake level was too high; therefore any plan must be constrained to avoid flooding this town (which incidentally had a very nice hotel where the O.R. people enjoyed their meals). Second, the new reservoir would have recreational facilities; sailing, fishing, and footpaths to permit visitors to enjoy the mountain scenery. All of these benefits to the environment depended on the reservoir being full. Third, although the people living by the river did not want to be flooded, they also did not want the river level to be "just below flood level" for lengthy periods, as this made the fields beside the river waterlogged.

So the O.R. people realised that there were two parts to the problem; there was a long term water supply problem, and a short-term flood mitigation problem. So they constructed two models. The first used records of rainfall, month by month, to feed into a model which determined a "Target level" for the reservoir for each month of the year, lower in the wet winter months, higher in the dry summer months. If the level was below the monthly target, then the control said "bring it up by reducing the releases", and if it was above, then the control said "let it down by increasing releases". The second model was concerned with controlling the river flow during times of flood risk, and modelled the control policy, hour by hour, through simulated run-off and releases from the reservoir.

And the staff employed by the citizens of that city were pleased with the work of the O.R. people, and used their plans for both long-term and short-term control of the reservoir.

In due course, the land had a severe drought, but the people of the city did not run short of water, thanks to the skills of the engineers and the O.R. people.

Some of this work is described in a more formal way in: D.G.Jamieson, D.K.Smith and J.C.Wilkinson "Evaluation of Short-term Operational Policies for a Multipurpose Reservoir System" Journal of Hydrology28 p191-213 (1976)